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Journal articles on the topic 'Diffraction patterns'

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Published: 4 June 2021

Last updated: 24 January 2023

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Gupta, Vipul K., and Sean R. Agnew. "Indexation and misorientation analysis of low-quality Laue diffraction patterns." Journal of Applied Crystallography 42, no. 1 (2009): 116–24. http://dx.doi.org/10.1107/s0021889808042349.

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A Laue X-ray diffraction pattern indexing scheme, similar to a method previously proposed for convergent beam and backscattered electron diffraction patterns, was implemented. Experimental diffraction patterns are compared with simulated templates corresponding to crystals of prescribed orientations. The orientation of a diffracting volume is determined by maximizing a normalized cross correlation index between experimental and theoretical patterns. The advantages of template matching include (i) elimination of the requirement for extensive peak search/fitting analysis; (ii) the ability to index overlapped diffraction patterns obtained from neighboring grains or second phase particles; and (iii) the ability to confidently index patterns of low quality. A best fit orientation can then be determined by a least-squares fitting approach based on singular value decomposition. The misorientation within a diffracting volume is calculated from `smeared' and/or `split' Laue patterns. The methodologies developed are illustrated using micro-Laue diffraction data obtained from the wake of a fatigue crack.

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Rioux, Frank. "Calculating diffraction patterns." European Journal of Physics 24, no. 3 (2003): N1—N3. http://dx.doi.org/10.1088/0143-0807/24/3/401.

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DePino, Andrew. "Unusual diffraction patterns." Physics Teacher 25, no. 4 (1987): 219–20. http://dx.doi.org/10.1119/1.2342224.

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Wright, S. I. "Automatic idexing of electron-backscatter diffraction patterns." Proceedings, annual meeting, Electron Microscopy Society of America 52 (1994): 598–99. http://dx.doi.org/10.1017/s0424820100170724.

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A typical Backscatter Kikuchi Diffraction pattern (BKD, also referred to in the literature as an EBSP or a BEKP) is shown in figure 1. Since the bands in the pattern represent planes in the diffracting volume, the lattice orientation can be determined from their geometrical arrangement. The task of correctly orienting a BKD can be broken into two parts: 1) finding the salient features in the pattern (either the diffraction bands or the intersections of the bands) and 2) using these features to determine the lattice orientation. Recent advances in feature detection in BKDs along with methods for digital image enhancement will be described in some detail. The determination of orientation from a set of detected bands (or intersections of bands) will also be discussed.Dingley has demonstrated that lattice orientation can be practically obtained from BKDs by imaging the diffraction patterns using a low light level video camera and indexing the patterns with the aid of an online computer.

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Lee, R. A., D. F. Lynch, and I. J. Wilson. "Diffraction Patterns of Generalized Curvilinear Diffraction Gratings." Optica Acta: International Journal of Optics 32, no. 5 (1985): 573–93. http://dx.doi.org/10.1080/713821766.

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Hurley, Noah, Steve Kamau, Khadijah Alnasser, Usha Philipose, Jingbiao Cui, and Yuankun Lin. "Laser Diffraction Zones and Spots from Three-Dimensional Graded Photonic Super-Crystals and Moiré Photonic Crystals." Photonics 9, no. 6 (2022): 395. http://dx.doi.org/10.3390/photonics9060395.

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The laser diffraction from periodic structures typically shows isolated and sharp point patterns at zeroth and ±nth orders. Diffraction from 2D graded photonic super-crystals (GPSCs) has demonstrated over 1000 spots due to the fractional diffractions. Here, we report the holographic fabrication of three types of 3D GPSCs through nine beam interferences and their characteristic diffraction patterns. The diffraction spots due to the fractional orders are merged into large-area diffraction zones for these three types of GPSCs. Three distinguishable diffraction patterns have been observed: (a) 3 × 3 Diffraction zones for GPSCs with a weak gradient in unit super-cell, (b) 5 × 5 non-uniform diffraction zones for GPSCs with a strong modulation in long period and a strong gradient in unit super-cell, (c) more than 5 × 5 uniform diffraction zones for GPSCs with a medium gradient in unit super-cell and a medium modulation in long period. The GPSCs with a strong modulation appear as moiré photonic crystals. The diffraction zone pattern not only demonstrates a characterization method for the fabricated 3D GPSCs, but also proves their unique optical properties of the coupling of light from zones with 360° azimuthal angles and broad zenith angles.

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McCarthy, G. J., J. M. Holzer, W. M. Syvinski, K. J. Martin, and R. G. Garvey. "Evaluation of Reference X-ray Diffraction Patterns in the ICDD Powder Diffraction File." Advances in X-ray Analysis 34 (1990): 369–76. http://dx.doi.org/10.1154/s0376030800014683.

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AbstractProcedures and tools for evaluation of reference x-ray powder patterns in the JCPDSICDD Powder Diffraction File are illustrated by a review of air-stable binary oxides. The reference patterns are evaluated using an available microcomputer version of the NBS*A1DS83 editorial program and PDF patterns retrieved directly from the CD-ROM in the program's input format. The patterns are compared to calculated and experimental diffractograms. The majority of the oxide patterns have been found to be in good agreement with the calculated and observed diffractograms, but are often missing some weak reflections routinely observed with a modern diffractometer. These weak reflections are added to the PDF pattern. For the remainder of the phases, patterns are redetermined.

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Liu, Hongwei, Matthew Foley, Qingyun Lin, and Jiangwen Liu. "EDP2XRD: a computer program for converting electron diffraction patterns into X-ray diffraction patterns." Journal of Applied Crystallography 49, no. 2 (2016): 636–41. http://dx.doi.org/10.1107/s1600576716000613.

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Mny commercial software packages for X-ray diffraction pattern analysis are capable of identifying multiple phases in bulk materials. However, X-ray diffraction patterns cannot record those phases with very small volume ratio or non-homogeneous distribution, which may mean that researchers have to use instead electron diffraction patterns from a very small region of interest. EDP2XRD, a new program for converting electron diffraction patterns into X-ray diffraction patterns, is described here. The program has been developed in order to utilize X-ray analysis software for electron diffraction patterns taken from mixed-phase nanocrystalline materials with a transmission electron microscope. It is specifically designed for material researchers who are engaged in crystallographic microstructure analysis. The difference from other popular commercial software for crystallography is that this program provides new options to convert and plot X-ray diffraction patterns for arbitrary electron diffraction rings and to process raw images to enhance conversion performance. The program contains the necessary crystallographic calculator to list planar d spacings and corresponding X-ray diffraction angles.

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Andrés, P., J. Lancis, E. E. Sicre, and E. Bonet. "Achromatic Fresnel diffraction patterns." Optics Communications 104, no. 1-3 (1993): 39–45. http://dx.doi.org/10.1016/0030-4018(93)90102-b.

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Smith, Deane K., Gerald G. Johnson, Alexandre Scheible, Andrew M. Wims, Jack L. Johnson, and Gregory Ullmann. "Quantitative X-Ray Powder Diffraction Method Using the Full Diffraction Pattern." Powder Diffraction 2, no. 2 (1987): 73–77. http://dx.doi.org/10.1017/s0885715600012409.

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AbstractA new quantitative X-ray powder diffraction (QXRPD) method has been developed to analyze polyphase crystalline mixtures. The unique approach employed in this method is the utilization of the full diffraction pattern of a mixture and its reconstruction as a weighted sum of diffraction patterns of the component phases. To facilitate the use of the new method, menu-driven interactive computer programs with graphics have been developed for the VAX series of computers. The analyst builds a reference database of component diffraction patterns, corrects the patterns for background effects, and determines the appropriate reference intensity ratios. This database is used to calculate the weight fraction of each phase in a mixture by fitting its diffraction pattern with a least-squares best-fit weighted sum of selected database reference patterns.The new QXRPD method was evaluated using oxides found in ceramics, corrosion products, and other materials encountered in the laboratory. Experimental procedures have been developed for sample preparation and data collection for reference samples and unknowns. Prepared mixtures have been used to demonstrate the very good results that can be obtained with this method.

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Martin, A. V., A. J. Morgan, T. Ekeberg, et al. "The extraction of single-particle diffraction patterns from a multiple-particle diffraction pattern." Optics Express 21, no. 13 (2013): 15102. http://dx.doi.org/10.1364/oe.21.015102.

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Bošnjaković, Dejan, Marko Gregorc, Hui Li, Martin Čopič, Valentina Domenici, and Irena Drevenšek-Olenik. "Mechanical Manipulation of Diffractive Properties of Optical Holographic Gratings from Liquid Crystalline Elastomers." Applied Sciences 8, no. 8 (2018): 1330. http://dx.doi.org/10.3390/app8081330.

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An appealing property of optical diffractive structures from elastomeric materials is a possibility to regulate their optical patterns and consequently also their diffractive features with mechanical straining. We investigated the effect of strain on diffraction characteristics of holographic gratings recorded in a monodomain side-chain liquid crystalline elastomer. The strain was imposed either parallel or perpendicular to the initial alignment direction of the material. At temperatures far below the nematic–paranematic phase transition, straining along the initial alignment affects mainly the diffraction pattern, while the diffraction efficiency remains almost constant. In contrast, at temperatures close to the nematic–paranematic phase transition, the diffraction efficiency is also significantly affected. Straining in the direction perpendicular to the initial alignment strongly and diversely influences both the diffraction pattern and the diffraction efficiency. The difference between the two cases is attributed to shear–stripe domains, which form only during straining perpendicular to the initial alignment and cause optical diffraction that competes with the diffraction from the holographic grating structure.

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Callahan, Patrick G., and Marc De Graef. "Dynamical Electron Backscatter Diffraction Patterns. Part I: Pattern Simulations." Microscopy and Microanalysis 19, no. 5 (2013): 1255–65. http://dx.doi.org/10.1017/s1431927613001840.

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AbstractA new approach for the simulation of dynamic electron backscatter diffraction (EBSD) patterns is introduced. The computational approach merges deterministic dynamic electron-scattering computations based on Bloch waves with a stochastic Monte Carlo (MC) simulation of the energy, depth, and directional distributions of the backscattered electrons (BSEs). An efficient numerical scheme is introduced, based on a modified Lambert projection, for the computation of the scintillator electron count as a function of the position and orientation of the EBSD detector; the approach allows for the rapid computation of an individual EBSD pattern by bi-linear interpolation of a master EBSD pattern. The master pattern stores the BSE yield as a function of the electron exit direction and exit energy and is used along with weight factors extracted from the MC simulation to obtain energy-weighted simulated EBSD patterns. Example simulations for nickel yield realistic patterns and energy-dependent trends in pattern blurring versus filter window energies are in agreement with experimental energy-filtered EBSD observations reported in the literature.

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Minemoto, Takumi, and Junzo Narano. "Hybrid pattern recognition by features extracted from object patterns and Fraunhofer diffraction patterns." Applied Optics 24, no. 18 (1985): 2914. http://dx.doi.org/10.1364/ao.24.002914.

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Chapman, Henry N., Carl Caleman, and Nicusor Timneanu. "Diffraction before destruction." Philosophical Transactions of the Royal Society B: Biological Sciences 369, no. 1647 (2014): 20130313. http://dx.doi.org/10.1098/rstb.2013.0313.

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X-ray free-electron lasers have opened up the possibility of structure determination of protein crystals at room temperature, free of radiation damage. The femtosecond-duration pulses of these sources enable diffraction signals to be collected from samples at doses of 1000 MGy or higher. The sample is vaporized by the intense pulse, but not before the scattering that gives rise to the diffraction pattern takes place. Consequently, only a single flash diffraction pattern can be recorded from a crystal, giving rise to the method of serial crystallography where tens of thousands of patterns are collected from individual crystals that flow across the beam and the patterns are indexed and aggregated into a set of structure factors. The high-dose tolerance and the many-crystal averaging approach allow data to be collected from much smaller crystals than have been examined at synchrotron radiation facilities, even from radiation-sensitive samples. Here, we review the interaction of intense femtosecond X-ray pulses with materials and discuss the implications for structure determination. We identify various dose regimes and conclude that the strongest achievable signals for a given sample are attained at the highest possible dose rates, from highest possible pulse intensities.

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Zuo, J. M., H. R. Zhu, and Andrew Spence. "Simulating electron microscope diffraction mode with a Macintosh-based program." Proceedings, annual meeting, Electron Microscopy Society of America 51 (August 1, 1993): 1210–11. http://dx.doi.org/10.1017/s042482010015188x.

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With the recent trend towards to the quantification of electron diffraction patterns, there is an increasing need for simulating the geometry of convergent beam electron diffraction patterns, and especially the high order Laue zone (HOLZ) lines in such patterns. The simulation program is useful in the way that the simulated and the experimental pattern can be compared, and then the important diffraction parameters such as reflection indices, beam directions and lattice constant could be found and used. Here we describe a Macintosh based program, which simulates electron diffraction pattern in the same way as the operation of electron microscope diffraction mode. The program has a control panel with the ‘scroll bar’ control devices for x and y tilt of specimen stage, x and y deflection of diffraction pattern and camera length (see figure 1). The user can change the simulated diffraction pattern by changing the ‘control devices’ with a pointing device such as a mouse.

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Louër, D. "Indexing of Powder Diffraction Patterns." Materials Science Forum 79-82 (January 1991): 17–26. http://dx.doi.org/10.4028/www.scientific.net/msf.79-82.17.

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Parente, C. B. R., V. L. Mazzocchi, S. Metairon, J. M. Sasaki, and L. P. Cardoso. "Symmetry in multiple diffraction patterns." Acta Crystallographica Section A Foundations of Crystallography 52, a1 (1996): C553. http://dx.doi.org/10.1107/s0108767396077446.

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Baake, M., D. Frettlöh, and U. Grimm. "Pinwheel patterns and powder diffraction." Philosophical Magazine 87, no. 18-21 (2007): 2831–38. http://dx.doi.org/10.1080/14786430601057953.

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Ferrer, J. L., M. Roth, and A. Antoniadis. "Data Compression for Diffraction Patterns." Acta Crystallographica Section D Biological Crystallography 54, no. 2 (1998): 184–99. http://dx.doi.org/10.1107/s0907444997007257.

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Daimon, Hiroshi, and Shozo Ino. "One-dimensional circular diffraction patterns." Surface Science 222, no. 1 (1989): 274–82. http://dx.doi.org/10.1016/0039-6028(89)90348-8.

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Daimon, Hiroshi, and Shozo Ino. "One-dimensional circular diffraction patterns." Surface Science Letters 222, no. 1 (1989): A548. http://dx.doi.org/10.1016/0167-2584(89)90205-3.

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Buck, Edgar C. "Interpreting Uranyl Mineral Diffraction Patterns." Microscopy and Microanalysis 4, S2 (1998): 560–61. http://dx.doi.org/10.1017/s1431927600022923.

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Secondary phases that form during the corrosion of nuclear waste forms may influence both the rate of waste form dissolution and the release of radionuclides [1]. The identification of these phases is critical in developing models for the corrosion behavior of nuclear waste forms. In particular, the secondary uranyl (VI) minerals that form during waste form alteration may control uranium solubility and release of radionuclides incorporated into these phases [2].The U6+ cation in uranyl minerals is almost always present as a linear (UO2)2+ ion [3]. This uranyl (Ur) ion is coordinated by four, five, or six anions (ϕ) in the equatorial plane resulting in the formation of square (Urϕ4), pentagonal (Urϕ5), and hexagonal (Urϕ6) bipyramids, respectively [3]. These bipyramid polyhedra may polymerize to form complex infinite sheet structures. The linking of Urϕ5 is observed in a number of uranyl minerals formed during waste glass and spent fuel corrosion [2,4], such as weeksite [Na,K(UO2)2(Si205)3*4H2O] and β-uranophane [Ca[(UO2)(SiO3OH)]2*5H2O].

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Baake, M., and D. Frettlöh. "SCD patterns have singular diffraction." Journal of Mathematical Physics 46, no. 3 (2005): 033510. http://dx.doi.org/10.1063/1.1842355.

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Eades, J. A., A. E. Smith, and D. F. Lynch. "convergent-beam diffraction from surfaces." Proceedings, annual meeting, Electron Microscopy Society of America 45 (August 1987): 30–33. http://dx.doi.org/10.1017/s0424820100125208.

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It is quite simple (in the transmission electron microscope) to obtain convergent-beam patterns from the surface of a bulk crystal. The beam is focussed onto the surface at near grazing incidence (figure 1) and if the surface is flat the appropriate pattern is obtained in the diffraction plane (figure 2). Such patterns are potentially valuable for the characterization of surfaces just as normal convergent-beam patterns are valuable for the characterization of crystals.There are, however, several important ways in which reflection diffraction from surfaces differs from the more familiar electron diffraction in transmission.GeometryIn reflection diffraction, because of the surface, it is not possible to describe the specimen as periodic in three dimensions, nor is it possible to associate diffraction with a conventional three-dimensional reciprocal lattice.

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Qin, L. C. "Electron diffraction from cylindrical nanotubes." Journal of Materials Research 9, no. 9 (1994): 2450–56. http://dx.doi.org/10.1557/jmr.1994.2450.

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Electron diffraction intensities from cylindrical objects can be conveniently analyzed using Bessel functions. Analytic formulas and geometry of the diffraction patterns from cylindrical carbon nanotubes are presented in general forms in terms of structural parameters, such as the pitch angle and the radius of a tubule. As an example the Fraunhofer diffraction pattern from a graphitic tubule of structure [18,2] has been simulated to illustrate the characteristics of such diffraction patterns. The validity of the projection approximation is also discussed.

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Schröder, Rasmus R., and Christoph Burmester. "Improvements in electron diffraction of frozen hydrated crystals by energy filtering and large-area single-electron detection." Proceedings, annual meeting, Electron Microscopy Society of America 51 (August 1, 1993): 666–67. http://dx.doi.org/10.1017/s0424820100149167.

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Diffraction patterns of 3D protein crystals embedded in vitrious ice are critical to record. Inelastically scattered electrons almost completely superimpose the diffraction pattern of crystals if the thickness of the crystal is higher than the mean free path of electrons in the specimen. Figure 1 shows such an example of an unfiltered electron diffraction pattern from a frozen hydrated 3D catalase crystal. However, for thin 2D crystals electron diffraction has been the state of the art method to determine the Fourier amplitudes for reconstructions to atomic level, and in one case the possibility of obtaining Fourier phases from diffraction patterns has been studied. One of the main problems could be the background in the diffraction pattern due to inelastic scattering and the recording characteristics for electrons of conventional negative material.It was pointed out before, that the use of an energy filtered TEM (EFTEM) and of the Image Plate as a large area electron detector gives considerable improvement for detection of diffraction patterns.

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Watier, Yves, and Andrew N. Fitch. "Protein Powder Diffraction Analysis with TOPAS." Materials Science Forum 651 (May 2010): 117–29. http://dx.doi.org/10.4028/www.scientific.net/msf.651.117.

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While various software packages exist to study powder patterns, few are accessible to beginners and yet remain highly customisable. In this paper we will give guidelines for biologists interested in analysing powder patterns of proteins with Topas. Several topics will be discussed, from basic methods like indexing on a restricted list of spacegroups, to advanced use of command input les for pattern modelling and rigid body renement.

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Sullenger, D. B., J. S. Cantrell, and T. A. Beiter. "X-ray powder diffraction patterns of energetic materials." Powder Diffraction 9, no. 1 (1994): 2–14. http://dx.doi.org/10.1017/s088571560001962x.

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X-ray powder diffraction patterns for 18 phases of 14 well-known explosives have been developed in our laboratory. Experimental patterns were obtained with an automated diffractometer for those phases for which samples were available. For phases with known crystal structures, patterns were calculated from the lattice and atomic positional parameters for comparison with the experimental patterns. Eleven of the experimental patterns have been included in Powder Diffraction File (PDF) Sets 40 and 42; four have been accepted but not yet issued. A final experimental pattern shall be submitted this year. In two other instances, since samples of sufficient quantity and/or quality were not available, calculated patterns alone are considered here. A review of the development of the crystallographic knowledge of these substances is given here together with a critique of the patterns and other known patterns of these phases.

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McCarthy, G. J., D. G. Grier, and P. Bayliss. "Upgrading Sulfide Mineral Patterns for the ICDD Powder Diffraction File." Advances in X-ray Analysis 38 (1994): 107–15. http://dx.doi.org/10.1154/s0376030800017705.

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Abstract The majority of sulfide mineral patterns in the International Centre for Diffraction Data Mineral Powder Diffraction File have historically been of low quality (e.g., FN &lt; 10 and qualitative intensities). A five-year study has resulted in upgrading approximately 20% of the poorer quality patterns and will triple the number of “star quality” patterns. This paper describes the experimental methods used to obtain these upgraded patterns. The essential role of diffraction pattern calculations and diffractogram simulations is stressed.

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Chen, Yu H., Se Un Park, Dennis Wei, et al. "A Dictionary Approach to Electron Backscatter Diffraction Indexing." Microscopy and Microanalysis 21, no. 3 (2015): 739–52. http://dx.doi.org/10.1017/s1431927615000756.

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AbstractWe propose a framework for indexing of grain and subgrain structures in electron backscatter diffraction patterns of polycrystalline materials. We discretize the domain of a dynamical forward model onto a dense grid of orientations, producing a dictionary of patterns. For each measured pattern, we identify the most similar patterns in the dictionary, and identify boundaries, detect anomalies, and index crystal orientations. The statistical distribution of these closest matches is used in an unsupervised binary decision tree (DT) classifier to identify grain boundaries and anomalous regions. The DT classifies a pattern as an anomaly if it has an abnormally low similarity to any pattern in the dictionary. It classifies a pixel as being near a grain boundary if the highly ranked patterns in the dictionary differ significantly over the pixel’s neighborhood. Indexing is accomplished by computing the mean orientation of the closest matches to each pattern. The mean orientation is estimated using a maximum likelihood approach that models the orientation distribution as a mixture of Von Mises–Fisher distributions over the quaternionic three sphere. The proposed dictionary matching approach permits segmentation, anomaly detection, and indexing to be performed in a unified manner with the additional benefit of uncertainty quantification.

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Slouf, Miroslav, Radim Skoupy, Ewa Pavlova, and Vladislav Krzyzanek. "Powder Nano-Beam Diffraction in Scanning Electron Microscope: Fast and Simple Method for Analysis of Nanoparticle Crystal Structure." Nanomaterials 11, no. 4 (2021): 962. http://dx.doi.org/10.3390/nano11040962.

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We introduce a novel scanning electron microscopy (SEM) method which yields powder electron diffraction patterns. The only requirement is that the SEM microscope must be equipped with a pixelated detector of transmitted electrons. The pixelated detectors for SEM have been commercialized recently. They can be used routinely to collect a high number of electron diffraction patterns from individual nanocrystals and/or locations (this is called four-dimensional scanning transmission electron microscopy (4D-STEM), as we obtain two-dimensional (2D) information for each pixel of the 2D scanning array). Nevertheless, the individual 4D-STEM diffractograms are difficult to analyze due to the random orientation of nanocrystalline material. In our method, all individual diffractograms (showing randomly oriented diffraction spots from a few nanocrystals) are combined into one composite diffraction pattern (showing diffraction rings typical of polycrystalline/powder materials). The final powder diffraction pattern can be analyzed by means of standard programs for TEM/SAED (Selected-Area Electron Diffraction). We called our new method 4D-STEM/PNBD (Powder NanoBeam Diffraction) and applied it to three different systems: Au nano-islands (well diffracting nanocrystals with size ~20 nm), small TbF3 nanocrystals (size < 5 nm), and large NaYF4 nanocrystals (size > 100 nm). In all three cases, the STEM/PNBD results were comparable to those obtained from TEM/SAED. Therefore, the 4D-STEM/PNBD method enables fast and simple analysis of nanocrystalline materials, which opens quite new possibilities in the field of SEM.

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Chushkin, Y., and F. Zontone. "Upsampling speckle patterns for coherent X-ray diffraction imaging." Journal of Applied Crystallography 46, no. 2 (2013): 319–23. http://dx.doi.org/10.1107/s0021889813003117.

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Coherent X-ray diffraction imaging is a lensless imaging technique where an iterative phase-retrieval algorithm is applied to the speckle pattern, the far-field diffraction pattern produced by an isolated object. To ensure convergence to a unique solution, the diffraction pattern must be oversampled by a factor of two or more. Since the resolution in real space depends on the maximum wave vector where the intensity is detected,i.e.on the detector field of view, there is a practical limitation on oversampling in reciprocal space and resolution in real space that is ultimately determined by the number of pixels. This work shows that it is possible to reduce the effective pixel size and maintain the detector field of view by applying a linear combination method to shifted diffraction patterns. The feasibility of the method is demonstrated by reconstructing the images of test objects from diffraction patterns oversampled in each dimension by factors of 1.3 and 1.8 only. The described approach can be applied to any diffraction or imaging technique where the resolution is compromised by a large pixel size.

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Koch, C., and J. C. H. Spence. "Reconstruction of the Projected Potential from a through Voltage Series of Dynamical Electron Diffraction Patterns Including Absorption." Microscopy and Microanalysis 7, S2 (2001): 914–15. http://dx.doi.org/10.1017/s1431927600030646.

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Recently several different methods have been proposed to reconstruct the projected crystal potential from electron diffraction patterns. These methods envolve either diffraction patterns at many different orientations (as many orientations as beams in the pattern) and/or images, which makes their experimental realization difficult. We propose an entirely new method for reconstructing the projected crystal potential from fully dynamical [including absorption and multiple scattering effects to all orders] diffraction patterns from only a single crystal orientation and no image at all. Knowledge of the specimen thickness is not necessary. However, it requires diffraction patterns at many different accelarating voltages, which is a parameter that can easily be varied (within a certain range) in most modern electron microscopes. Since the intensities in the electron diffraction pattern are not affected by lens abberations this method is capable of reconstructing the projected potential with a resolution far better than that of any method using HRTEM images.

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Boullay, P., L. Lutterotti, D. Chateigner, and L. Sicard. "Fast microstructure and phase analyses of nanopowders using combined analysis of transmission electron microscopy scattering patterns." Acta Crystallographica Section A Foundations and Advances 70, no. 5 (2014): 448–56. http://dx.doi.org/10.1107/s2053273314009930.

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The full quantitative characterization of nanopowders using transmission electron microscopy scattering patterns is shown. This study demonstrates the feasibility of the application of so-called combined analysis, a global approach for phase identification, structure refinement, characterization of anisotropic crystallite sizes and shapes, texture analysis and texture variations with the probed scale, using electron diffraction patterns of TiO2and Mn3O4nanocrystal aggregates and platinum films. Electron diffraction pattern misalignments, positioning, and slight changes from pattern to pattern are directly integrated and refined within this approach. The use of a newly developed full-pattern search–match methodology for phase identification of nanopowders and the incorporation of the two-wave dynamical correction for diffraction patterns are also reported and proved to be efficient.

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Nolze, Gert, Tomasz Tokarski, Łukasz Rychłowski, Grzegorz Cios, and Aimo Winkelmann. "Crystallographic analysis of the lattice metric (CALM) from single electron backscatter diffraction or transmission Kikuchi diffraction patterns." Journal of Applied Crystallography 54, no. 3 (2021): 1012–22. http://dx.doi.org/10.1107/s1600576721004210.

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A new software is presented for the determination of crystal lattice parameters from the positions and widths of Kikuchi bands in a diffraction pattern. Starting with a single wide-angle Kikuchi pattern of arbitrary resolution and unknown phase, the traces of all visibly diffracting lattice planes are manually derived from four initial Kikuchi band traces via an intuitive graphical user interface. A single Kikuchi bandwidth is then used as reference to scale all reciprocal lattice point distances. Kikuchi band detection, via a filtered Funk transformation, and simultaneous display of the band intensity profile helps users to select band positions and widths. Bandwidths are calculated using the first derivative of the band profiles as excess-deficiency effects have minimal influence. From the reciprocal lattice, the metrics of possible Bravais lattice types are derived for all crystal systems. The measured lattice parameters achieve a precision of <1%, even for good quality Kikuchi diffraction patterns of 400 × 300 pixels. This band-edge detection approach has been validated on several hundred experimental diffraction patterns from phases of different symmetries and random orientations. It produces a systematic lattice parameter offset of up to ±4%, which appears to scale with the mean atomic number or the backscatter coefficient.

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Nishiyama, Toshiyuki, Akinobu Niozu, Christoph Bostedt, et al. "Refinement for single-nanoparticle structure determination from low-quality single-shot coherent diffraction data." IUCrJ 7, no. 1 (2020): 10–17. http://dx.doi.org/10.1107/s2052252519014222.

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With the emergence of X-ray free-electron lasers, it is possible to investigate the structure of nanoscale samples by employing coherent diffractive imaging in the X-ray spectral regime. In this work, we developed a refinement method for structure reconstruction applicable to low-quality coherent diffraction data. The method is based on the gradient search method and considers the missing region of a diffraction pattern and the small number of detected photons. We introduced an initial estimate of the structure in the method to improve the convergence. The present method is applied to an experimental diffraction pattern of an Xe cluster obtained in an X-ray scattering experiment at the SPring-8 Angstrom Compact free-electron LAser (SACLA) facility. It is found that the electron density is successfully reconstructed from the diffraction pattern with a large missing region, with a good initial estimate of the structure. The diffraction pattern calculated from the reconstructed electron density reproduced the observed diffraction pattern well, including the characteristic intensity modulation in each ring. Our refinement method enables structure reconstruction from diffraction patterns under difficulties such as missing areas and low diffraction intensity, and it is potentially applicable to the structure determination of samples that have low scattering power.

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Steele, James K., and Ronald R. Biederman. "Powder Diffraction Pattern Simulation and Analysis." Advances in X-ray Analysis 37 (1993): 101–7. http://dx.doi.org/10.1154/s0376030800015561.

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The graphics capability and speed available in modern personal computers has encouraged an increase in the use of a direct pattern comparison approach to the analysis of x-ray and electron diffraction patterns. Several researchers over the past 30 years have presented programs and algorithms which calculate and display powder patterns for xray diffraction. These programs originally required a main frame computer which was expensive and generally not available to all researchers. With the recent advances in the speed of personal computers, language compilers, and high resoultion graphics, expecially within the past 5 years, real time calculations and display of calculated patterns is becoming widely available. The power of this approach will be demonstrated through the use of an IBM compatable personal computer code developed by the authors.

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Jackson, Brian E., Jordan J. Christensen, Saransh Singh, et al. "Performance of Dynamically Simulated Reference Patterns for Cross-Correlation Electron Backscatter Diffraction." Microscopy and Microanalysis 22, no. 4 (2016): 789–802. http://dx.doi.org/10.1017/s143192761601148x.

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AbstractHigh-resolution (or “cross-correlation”) electron backscatter diffraction analysis (HR-EBSD) utilizes cross-correlation techniques to determine relative orientation and distortion of an experimental electron backscatter diffraction pattern with respect to a reference pattern. The integrity of absolute strain and tetragonality measurements of a standard Si/SiGe material have previously been analyzed using reference patterns produced by kinematical simulation. Although the results were promising, the noise levels were significantly higher for kinematically produced patterns, compared with real patterns taken from the Si region of the sample. This paper applies HR-EBSD techniques to analyze lattice distortion in an Si/SiGe sample, using recently developed dynamically simulated patterns. The results are compared with those from experimental and kinematically simulated patterns. Dynamical patterns provide significantly more precision than kinematical patterns. Dynamical patterns also provide better estimates of tetragonality at low levels of distortion relative to the reference pattern; kinematical patterns can perform better at large values of relative tetragonality due to the ability to rapidly generate patterns relating to a distorted lattice. A library of dynamically generated patterns with different lattice parameters might be used to achieve a similar advantage. The convergence of the cross-correlation approach is also assessed for the different reference pattern types.

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Dingley, D. J., A. J. Wilkinson, and G. P. Burns. "Strain measurements using electron backscattering diffraction patterns." Proceedings, annual meeting, Electron Microscopy Society of America 48, no. 4 (1990): 402–3. http://dx.doi.org/10.1017/s0424820100175144.

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The Electron Backscatter Diffraction (EBSP) technique, first applied to the Scanning Electron Microscope by Venables and Harland and later by Dingley et al., is now widely used, particularly for crystal orientation determination , and for the determination of crystal symmetry,. Methods have also been sought to apply it for measurement of internal strain and this paper reviews and reports the findings. Plastic strain measurements from diffraction patterns obtained using the related selected area channelling technique have been widley reported and are reviewed in reference.Elastic and plastic strain in crystals causes a shift in the diffraction line positions, line broadening, and a decrease in diffracted intensity. Measurement of these changes in EBSP is hindered by several problems peculiar to the method. As the patterns are formed by Bragg scattering of initially ine1 astica11y scattered electrons, there is a natural line broadening arising from an energy spread in the diffracted electrons amounting to 1% of the incident beam energy. This is compounded by the fact that the Bragg angle for diffraction is generally less than 2° and that dynamical diffraction effects result in the diffraction profiles being highly assymetric with long tails. Consequently there is considerable overlapp of profiles. Other problems arise from the gnomonic projection of the pattern producing a distortion which increase towards the edges of the pattern and from the need to tilt the specimen towards the recording film which produces further asymmetry in the line profile. Finally, surface contamination is observed to degrade the diffraction pattern reducing line intensity in much the same way as plastic strain.

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Yogaswara, Yuri, and Fourier Dzar Eljabbar Latief. "Digital Image Analysis Of Single Rectangular Slit Fraunhofer Diffraction Patterns." Indonesian Journal of Physics 30, no. 2 (2019): 8–13. http://dx.doi.org/10.5614/itb.ijp.2019.30.2.2.

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Study of the single rectangular slit Fraunhofer diffraction pattern has been carried out through experiments. Data acquisition was done by manually measuring the distance of the bright and dark diffraction patterns using millimeter block paper and by means of digital images analysis of the diffraction patterns. The digital images were used to obtain the bright and dark intensity data of the pattern as the function of the distance from the center of the pattern. The process of obtaining the data was carried out as follows: image acquisition, image digitization, image quality enhancement, graphics plotting and chart normalization. The data processing is done analytically and computationally using ImageJ software. The results of the digital image analysis of diffraction patterns produce an intensity graph of the distance of the diffraction pattern (I-y chart). The results from the digital image analysis approach provide an alternative method that is more accurate in the process of calculating the physical magnitude of diffraction parameters such as the wavelength of the source. One of the advantages of this method is that intensity of the diffraction pattern can be visualized as a function of the distance from the center of the screen. Although accuracy of the calculation result is not very high, the magnitude of the intensity can be observed to decrease with increasing distance of the diffraction pattern to the center of the screen. The results of the calculation of the source wavelength by means of digital image analysis provides good results compared to the manual method using the millimeter block paper. The smallest mean error of the wavelength by means of digital image analysis is 1,72% and the manual method using the millimeter block paper is 3,84%. This method of measurement using digital image analysis can be used as an alternative for various position or distance-based measurement, such as the calculation of linear expansion coefficient with a single slit diffraction method.

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Wu, Jinsong, and John C. H. Spence. "Low-Dose, Low-Temperature Convergent-Beam Electron Diffraction and Multiwavelength Analysis of Hydrocarbon Films by Electron Diffraction." Microscopy and Microanalysis 9, no. 5 (2003): 428–41. http://dx.doi.org/10.1017/s1431927603030368.

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Aromatic hydrocarbon (perylene, coronene) and tetracontane films are shown to produce useful convergent-beam electron diffraction (CBED) patterns under low-dose and low-temperature conditions. These were obtained using a Zeiss LEO-921 electron microscope with an omega energy filter at liquid helium and nitrogen temperatures. The usefulness of patterns showing CBED disks of constant intensity (“blank disks,” indicating kinematic scattering) for structure analysis is investigated, with the aim of avoiding film-bending artifacts. Using CBED patterns from thicker areas, sample thickness was experimentally determined using either two-beam or three-beam patterns. Koehler mode illumination (a new form of SAD pattern offering smaller areas) was also used, and the possibility of obtaining structure factor moduli using the kinematic and two-beam approximations was investigated by comparing measured diffraction intensities with experimental ones for these known structures. The commonly used approximation |F| ∼ Ig (intended to account for bending) was found to be a worse approximation than the two-beam approximation with well-defined excitation error for these microdiffraction experiments. A new multiwavelength method of retrieving structure factor moduli and thickness from microdiffraction patterns using two-beam theory is demonstrated for tetracontane.

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Sutliff, J. A., and M. R. Notis. "Electron diffraction analysis using a personal computer." Proceedings, annual meeting, Electron Microscopy Society of America 47 (August 6, 1989): 54–55. http://dx.doi.org/10.1017/s0424820100152240.

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The analysis of electron diffraction patterns (EDPs) by manual calculation is difficult in two important cases. The first is when there are many phases that must be included in the search for a pattern’s solution. The second is when, due to the structure of the phases being considered, many solutions for a pattern are possible. In these cases, it is very time consuming to ensure that all possible solutions are found and that the best solution is chosen. A computer can provide tremendous help for the EDP analyst in these situations. Through its ability to make rapid calculations and display data graphically, a computer can relieve the analyst of much of the work involved in a thorough electron diffraction analysis.In analyzing EDPs a standard procedure is adopted. The analyst first assembles a data base of phases that could be present in the sample being studied. Tables of interplanar spacings and interplanar angles are calculated from crystal structure data on each phase. The positions of spots on experimental patterns are then recorded and radii from the transmitted beam spot to diffracted beams’ spots are measured. Ratios of radii and angles between radii are tabulated.

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Michael, J. R., and R. P. Goehner. "Reduced Unit Cell Determination From Unindexed EBSD Patterns." Microscopy and Microanalysis 6, S2 (2000): 946–47. http://dx.doi.org/10.1017/s1431927600037223.

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Electron backscatter diffraction (EBSD) is a technique that can provide identification of unknown crystalline phases while exploiting the excellent imaging capabilities of the scanning electron microscope (SEM). Phase identification using EBSD has now progressed to the point that it is commercially available. Phase identification in the SEM requires high quality EBSD patterns that can only be collected using either film or charge coupled device (CCD)-based cameras. High quality EBSD patterns obtained in this manner show many diffraction features that are useful in the determination of the unit cell of the sample.’ This paper will discuss the features in the EBSD patterns and the procedure used to determine the reduced unit cell of the sample.One of the major advantages of EBSD over electron diffraction in the transmission electron microscope is the remarkable field of view that is routinely attained. The large angular view of the diffraction pattern permits many zone axes and their associated symmetries to be viewed in a single pattern or at most a few patterns.

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Ravy, Sylvain. "Order as revealed by coherent diffraction." Acta Crystallographica Section A Foundations and Advances 70, a1 (2014): C525. http://dx.doi.org/10.1107/s2053273314094741.

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We are generally taught that a crystal is disordered if its diffraction pattern consists in Bragg reflections and diffuse scattering. However, more insight in the diffraction theory shows that a crystal can be perfectly ordered and still exhibit diffuse scattering. This is the case of the Rudin-Shapiro sequence, whose pair correlation function is similar to a random sequence one. In this paper, we show that this is true only for the infinite sequence. Indeed, finite crystals exhibit speckles patterns which can be measured by coherent diffraction. With the help of the Rudin-Shapiro sequence, we demonstrate that the intensity distribution of such patterns contains information on high order correlation functions, which are irrelevant in infinite crystal diffuse scattering pattern. This surprising result indicates that the concept of order should be revisited in the light of coherent beams.

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Reardon, Brian J., and Camden R. Hubbard. "A Review of the XRD Data of the Phases Present in the CaO-SrO-PbO System." Powder Diffraction 7, no. 2 (1992): 96–98. http://dx.doi.org/10.1017/s0885715600018315.

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AbstractX-ray powder patterns for the phases in the CaO-SrO-PbO ternary system, along with the corresponding crystal structures, were obtained from the literature and from the Powder Diffraction File. Available XRD patterns were compared with each other and with a simulated pattern for each phase, yielding a recommended reference pattern. The simulated powder patterns presented here deal with the phases found within the (Ca,Sr)2PbO4solid solution series and are recommended for the Powder Diffraction File (PDF).

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McCarthy, Gregory J., Kyli J. Martin, Jean M. Holzer, Dean G. Grier, Wayne M. Syvinski, and Darred W. Nodland. "Calculated Patterns in X-Ray Powder Diffraction Analysis." Advances in X-ray Analysis 35, A (1991): 17–23. http://dx.doi.org/10.1154/s0376030800008624.

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AbstractCalculated patterns play an essential role in X-ray powder diffraction analysis. This paper gives examples of their use in qualitative analysis for evaluating and supplementing reference patterns in the ICDD Powder Diffraction File (PDF), in quantitative analysis for calculating Reference Intensity Ratios (RIRs), in ceil parameter refinements for indexing of low-symmetry/large unit cell diffractograms, in powder pattern determination for validating intensities and recognizing preferred orientation, in new materials synthesis for verification of structure type and phase purity, and for modeling the effects of solid solution substitution.

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Bright, David S., Alline F. Myers, Shirley Turner, and Eric B. Steel. "Spot Measurement Tool for Diffraction Pattern Analysis." Microscopy and Microanalysis 4, S2 (1998): 60–61. http://dx.doi.org/10.1017/s1431927600020420.

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Accurate characterization of electron diffraction patterns can be tedious, which encourages development of computer assisted tools and methods. We developed a spot measurement tool to characterize rapidly arrays of diffraction spots that are characteristic of a single crystal, and to measure precisely the d-spacing values for individual spots. The spot tool determines these vectors for averaged measurements from many spots in a digital image of the diffraction pattern. Previously we developed automated methods for spot pattern analysis. Why make an operator-assisted tool? This tool is faster than either our automated or entirely manual methods, and it allows assessment of the quality of the data at the beginning of the analysis.It is easy to see regular patterns of spots in a zone axis diffraction pattern (Fig. 1.1). An operator guides the initial calculations by adjusting an array of circles to approximately cover the spots in the pattern to be analyzed.

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Zuo, J. M., and Y. F. Shi. "Complementary Structural Information from Diffraction Patterns in STEM: Accurate Thickness Measurement with Pattern Matching." Microscopy and Microanalysis 7, S2 (2001): 224–25. http://dx.doi.org/10.1017/s1431927600027197.

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In this paper, we discuss the advantage of combining STEM imaging with diffraction. in addition, we present a set of accurately calculated convergent beam electron diffraction (CBED) patterns for Si, which highlights the sensitivity of electron diffraction to structure. The calculation takes the full account of crystal bonding by including known experimental structure factors in simulation. Such calculated patterns can be used for accurate determination of the sample thickness, crystal orientation and polarity (for acentric crystals). Calculations with and without crystal bonding show significant difference in calculated intensities, equivalent to a change in thickness about several nanometers for thick samples.The annual dark field (ADF) imaging mode in scanning transmission electron microscopes offers the unique advantage of combining high-resolution electron imaging and spectroscopy with diffraction. The large cutoff angle used in ADF imaging allows simultaneous recording of diffraction patterns for quantitative structural information, while ADF imaging gives the precise position of the probe and the image of the sample.

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Petrov, V. A., and R. A. Ryutin. "Patterns of the exclusive double diffraction." Journal of Physics G: Nuclear and Particle Physics 35, no. 6 (2008): 065004. http://dx.doi.org/10.1088/0954-3899/35/6/065004.

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